GATE 2026 AE – Question 62
A gas mixture at a pressure of 800 kPa and a density of 5 kg/m$^3$ enters a turbine stage. The temperature of the gas at the nozzle exit and the stage exit are 790 K and 750 K, respectively. Assume the specific heats are constant for the gas mixture in the range of temperatures considered. The specific heat at constant pressure is 0.72 kJ/kg-K and the ratio of specific heats is 1.33. The value of the degree of reaction of the turbine stage is ________ (rounded off to 2 decimal places).
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Correct answer: 0.26 to 0.29
Explanation
The gas constant is $R = c_p\frac{\gamma - 1}{\gamma} = 0.72 \times \frac{0.33}{1.33} = 0.1787$ kJ/kg-K, so the inlet temperature is $T_1 = \frac{p}{\rho R} = \frac{800}{5 \times 0.1787} = 895.6$ K. The degree of reaction is the share of the stage enthalpy drop that takes place in the rotor: $\frac{T_2 - T_3}{T_1 - T_3} = \frac{790 - 750}{895.6 - 750} = 0.27$.
Official GATE 2026 answer key: https://gate2026.iitg.ac.in/doc/download/2026/Keys/AE_Keys.pdf